1. **State the problem:** We have two triangles STS and VUW with ST \parallel UW, and we need to find the value of $p$ given the side lengths: $UT=24$, $VU=26$, $VW=16p-3$, and $WS=p+11$. 2. **Use the Triangle Proportionality Theorem:** Since $ST \parallel UW$, the triangles are similar, so corresponding sides are proportional: $$\frac{UT}{VU} = \frac{VW}{WS}$$ 3. **Substitute the given lengths:** $$\frac{24}{26} = \frac{16p - 3}{p + 11}$$ 4. **Cross multiply:** $$24(p + 11) = 26(16p - 3)$$ 5. **Expand both sides:** $$24p + 264 = 416p - 78$$ 6. **Bring all terms to one side:** $$24p + 264 - 416p + 78 = 0$$ $$-392p + 342 = 0$$ 7. **Isolate $p$:** $$-392p = -342$$ $$p = \frac{\cancel{-}342}{\cancel{-}392}$$ 8. **Simplify the fraction:** Both numerator and denominator are divisible by 2: $$p = \frac{171}{196}$$ 9. **Final answer:** $$p = \frac{171}{196}$$